blender making empty parent as a child in cube parent
This has to be done in Object Mode. 

First select the object you want as a children (in your case, the empty). Hold SHIFT while you select the object you want to become the parent of the object you selected first (Note that the outline around your empty object should turn from a bright orange to a dark orange color).

Then press CTRL+P and select "Select parent to "Object"".

GIF illustrating the process:



Hope this helps.